The Role of Interest Rate Policy in the Generation and Propagationof Business Cycles: What Has Changed Since the 30’s?

by

Christopher A. Sims

Pre-conference draft #2, June 19, 1998

Post-conference draft revised August 19, 1998

1

IntroductionGovernments have two broad classes of macroeconomic impact. One has to do with the way

government liabilities, including cash, interact with other traded assets in the financial system.The other has to do with government absorption and production of real resources through non-neutral taxation and provision of government goods and services like roads, schooling and publichealth measures. There is some evidence that fluctuations in the latter class of impact areimportant1, and it can be shown theoretically that the effects could be substantial and are hard topin down quantitatively on the basis of a priori reasoning2. Policy discussion and themacroeconomic literature may have overemphasized the former, financial class of impacts.

Nonetheless, this paper focuses on the financial impact. It presents empirical evidence, similarto much that has appeared previously using time series statistical modeling, that only a smallportion of business cycle variation in the US since 1948 can be attributed to fluctuations inmonetary policy. Though this conclusion is not universally accepted, it is far from new. Thispaper therefore goes on to consider two additional possible ways of demonstrating importanteffects of monetary policy. It expands the usual time frame of the literature, extending its modelto the interwar period, and it examines the behavior of the model with counterfactual variations inthe equation describing policy behavior.

The paper presents evidence that the same methods of identifying the effects of monetarypolicy that have proved useful in the analysis of postwar US data can be applied to interwar data,where they show responses of the private sector to monetary policy shifts to have been quitesimilar then to what they are now. The fact that these methods prove robust in most respectsacross such widely varying historical circumstances provides additional support for their reliabilityin both periods.

The nature of private sector disturbances was different in these two periods, however, and thenature of monetary policy response to shocks also differed. During the interwar period shocksthat implied expected future price changes were not quickly met by countervailing monetarypolicy. Also, during the interwar period disturbances that resulted in a flow out of bank depositsinto currency were important. Such disturbances were met with interest rate increases, whichmight have exacerbated their effects on the banking system.

Experimentation with counterfactual specifications of policy behavior suggest that in bothperiods prices could have been kept more stable by a different monetary policy, but that there wasonly modest room for reducing cyclical fluctuations in output by modifying monetary policy.

Can we conclude that monetary policy has had little to do with the improved stability ofeconomic activity in the postwar period? Only if we construe monetary policy narrowly, as thenormal tightening and loosening of credit conditions associated with interest rate changes.Periods of financial crisis or “liquidity crunch” are treated by the modeling methods used here assurprises originating outside the policy process, but this is true only in a narrow sense. Beliefs of

1 See Garcia-Mila [1987]2 See Baxter and King [1993].

2

the public about the adequacy of bank supervisory regulation, about the central bank’scommitment to and capacity to act as lender of last resort and to prevent the kind of acceleratinginflation or deflation that ends in crisis, are determined by some aspects of monetary policy andinstitutions, though not by the month-to-month or year-to-year management of interest rate policyvia open market operations.3

It is in this latter aspect of monetary policy, its provision of a stable base for financial markets,that it is most fundamentally entangled with fiscal policy. The paper invokes the recentlyarticulated fiscal theory of the price level, which may provide some insight into the sources ofpolicy difficulties in the great depression and in recent international banking, monetary and fiscalcrises. This line of thinking also suggests reasons for the observed greater postwar financialstability in the US, as well as cautions concerning future developments in the US and internationalmonetary systems.

Though it is not essential to understanding the paper’s empirical evidence, it may be worthrecognizing here that the paper uses a somewhat different vocabulary and point of view than doesmuch macroeconomic policy discussion. We are not dividing the influences of government into“aggregate demand” and “aggregate supply” components as would the viewpoint of standardKeynesian hydraulics. Expectations of future monetary and fiscal policy can influence currentinflationary pressures without changing current real flows of expenditures. In contrast withstandard monetarist views, we are treating monetary and fiscal policy symmetrically, emphasizingthe point that the price level, the ratio at which government nominal liabilities trade for realcommodities, depends on the valuation of the entire portfolio of government assets. Thefundamental determinants of the price level do not depend on whether reserve requirements areeliminated or whether privately issued interest-bearing money replaces currency. And of coursethe entire focus of interest in the paper is on the possible inadequacy of a viewpoint, like that ofsimple real business cycle theory, that ignores the financial impact of the government onmacroeconomic fluctuations.

This “fiscal theory of the price level”, or FTPL, point of view has been articulated in agrowing stream of recent papers, e.g. Ben-Habib, Schmidt-Grohe, and Uribe [1998], Cochrane[1988], Leeper [1991], Woodford [1994], Woodford [1995], Sims [1994], and Sims [1997].While some of this literature has emphasized the possibility of seeing inflation as determinedprimarily or entirely by fiscal policy, the theory implies that with stable fiscal policy of a certainplausible form, interest rate policy conducted through open market operations can be the mainsource of government-generated fluctuations in inflationary and deflationary pressure, just as it isin conventional macroeconomic theory. This paper’s empirical work pursues this possibility. Thedistinctive FTPL point of view emerges mainly in the discussion of explanations outside themodels estimated for the behavior the models uncover.

3 Bernanke [1983] has argued for the importance of “non-monetary” financial mechanisms of

propagation in the great depression. The results in this paper confirm his, and indeed suggest lessimportance for interest rate and reserve policy than his discussion.

3

I. Monetary Policy and the Business Cycle

The reason the importance of monetary policy to cyclical fluctuations remains an unsettledissue is that observed data can offer no simple resolution of it. The money stock, bank reserves,and interest rates reflect events in financial markets, which in turn are sensitive to every kind ofimportant (and possibly also unimportant) influence on the economy. So while these variables arethe main levers of monetary policy, we can reach misleading conclusions by simply plotting orregressing measures of economic activity on these “policy variables”. Early monetarist empiricalresearch largely did just that, invoking an assumption that the money stock was properly regardedas determined by policy, with response of the money stock to disturbances originating in theprivate sector less important than independent variation in monetary policy.4 A plot of interestrates against output over the postwar period shows that interest rate rises preceded eachrecession. Some economists have taken the view that this leaves no room for doubt or subtlety:monetary policy must have produced the recessions. But as it has become standard to usemultivariate methods of time series analysis to characterize and interpret the data on interest rates,money stock, and business activity, it has become clear that simple bivariate interpretations of thedata are misleading. In fact the most likely interpretation of the data gives independent variationin monetary policy a modest role.

The literature that has reached this conclusion, concentrating mainly on postwar US data, isby now extensive. It has been surveyed recently in Leeper, Sims and Zha [1996]. Rather thanrepeat that summary, this paper begins by encapsulating the results of the literature in arepresentative model. The model is constructed with an eye to allowing its extension, withminimal need to change data definitions, to the interwar period. We consider the joint behavior ofsix monthly time series that can be collected in more or less comparable form for both postwarand interwar periods: Industrial production (IP), consumer price index (CPI), currency incirculation (Currency), currency plus demand deposits (M1), Federal Reserve discount rate(Discount), and a commodity price index (Pcomm).5 All variables are measured in natural logunits, except the discount rate, which is measured in percentage points.

The use of the discount rate as the interest rate variable does not match most of the literature.Since the persuasive article of Bernanke and Blinder [1992], the most widely used interest rate instudies of monetary policy has been the Federal Funds rate. However the Federal Funds marketdid not exist at the beginning of the postwar period. The discount window played a moreimportant role at the beginning of the interwar period than it has since, and the discount rate isprobably widely regarded as a lagging reflection of monetary policy in recent years. There areother interest rates, in particular the 4-6 month commercial paper rate, that are available over the

4 Milton Friedman wrote in 1958, “Changes in the money stock are a consequence as well as

an independent cause of changes in income and prices, though once they occur they will in theirturn produce still further effects on income and prices. This consideration blurs the relationbetween money and prices but does not reverse it. For there is much evidence…that even duringbusiness cycles the money stock plays a largely independent role.” (Friedman [1958].)

5 Some of these series required splicing of data from more than one source, so the reader isadvised at some point to look at the appendix describing the data in more detail.

4

full period of interest. However spreads between private and government interest rates weremore variable in the interwar period than they have been recently, and the degree to whichmonetary policy deliberately controlled private short rates was probably lower in the interwarperiod. Most of the calculations reported in this paper were carried out both with the 4-6 monthcommercial paper rate and with the discount rate. It is perhaps surprising that the results for thepostwar period turn out to be qualitatively unaffected by which rate is used. The fit of the modelfor variables other than the interest rate is slightly better in the postwar period with commercialpaper rate, but the statistics testing stability of the model across the postwar sample are slightlybetter for the version with the discount rate. In the interwar model, use of the commercial paperrate produces estimates that imply a brief, small, but statistically significant positive response of IPto a monetary contraction before the response turns negative. This no doubt reflects someinaccuracy in the identification of the model, and it leads to small anomalies in plots of results. Itis for these reasons that the presentation concentrates on results with the discount rate.

The notation for the model is

A L y t C tb g b g( ) = + ε , (1)

where y is the n ×1 column vector of variables in the model, A is a polynomial in the lag operator

L with n n× matrix coefficients Ai on the Li , C is a vector of constants, and ε is a vector ofrandom disturbances, serially uncorrelated, uncorrelated with y’s dated earlier, and withcorrelation matrix the identity. This notation is a little different from that most common in theliterature, in that it normalizes none of the coefficients in A0 to one, and correspondingly

normalizes the variances of the disturbances ε to one. Models with different A polynomials that

have the same values of the reduced-form coefficient polynomial B L A A L( ) = −0

1 b g and the same

value of the reduced-form residual covariance matrix Σ = ′A A0 0 imply the same distribution forthe data.

The model follows the existing literature in assuming a delay of at least one month in theimpact of interest rate changes on the private sector behavior that determines a block of variablesincluding IP and CPI. The contemporaneous correlation of interest rate changes with economicactivity tends to be positive; this assumption rules out the possibility that this positive correlationmight arise from a positive effect of monetary contraction on business activity. The assumption isjustified by the argument that the behavior of individual consumers, workers and businessmen thatdetermines industrial production and final goods prices does not involve continuous, sharp, finelycalculated responses to market signals. This is to some extent due to technologically determinedinertia, but probably more importantly to the lack of sufficient computational capacity on the partof individuals to make such continuous readjustments. Short-term fluctuations in money marketrates are not an important day-to-day influence on most non-financial economic decisions, notbecause people can’t look up the Federal Funds rate in the newspaper or because it would be very

5

difficult or expensive to react, but because people have too much else of greater personalimportance absorbing their attention.6

The model differs from most previous literature, and follows Leeper, Sims and Zha [1996], inincluding the money stock, and in this model also currency, in the block of variables determinedwithin the sluggish sector. The usual money demand or liquidity preference relation is derived asan arbitrage relation connecting returns on bonds to the implicit yield on money balances. Thederivation does not imply any lag in the relation. In treating currency and money this way,therefore, we are precluding a conventional money demand equation with no lags. However, thesame reasoning that justifies assuming sluggishness in the reaction of IP and CPI to financialmarket signals implies that we should expect similar delay in the reaction of individuals andbusinesses to financial signals that imply they should deliberately change holdings of cash anddemand deposits. Such holdings can of course react instantly to changes in flows of income andexpenditure – to the same disturbances, in other words, that act on IP and CPI. Other models inthe literature have produced reasonable results allowing for a money demand equation thatincludes a contemporaneous interest rate term. But it is difficult to justify a claim thatdisturbances to the aspects of private behavior that determine the money demand arbitragerelation should be unrelated to other shocks to private sector behavior. If money demand shocksare related to other shocks to private behavior, then the appearance of the interest rate in “moneydemand” must make it appear in all equations of the sluggish block, and this underminesidentification.

An identifying restriction that is particularly important in extending the model to the interwaryears is that the behavior of the Federal Reserve does not react within the month to IP or CPI.This does not mean that the Federal Reserve is assumed not to care about these variables. Itsimply reflects the fact that information on these variables is not available within the month. Thespecification does allow reaction by the Fed to these variables with a month’s delay, and it allowscontemporaneous reaction of the Fed to currency and M1, which the Fed monitors via itsregulatory role, and to Pcomm, which reflects publicly known prices in continuously functioningauction markets.

The pattern of restrictions we have discussed can be displayed in the matrix shown here asTable 1. In this table, X’s represent unconstrained coefficients in A0 , 0’s coefficients constrainedon the basis of behavioral reasoning, as given above, and -‘s represent coefficients constrained tozero as normalizations. Note that the first four equations, represented by the first four rows ofthe table, are distinguished only by normalizing restrictions. They do not have distinct behavioralinterpretations. Only the block of four equations, representing sluggish components of privatesector behavior, has an interpretation. The last row represents the reaction of commodity prices,in continuously clearing markets, to all current information.

6 In Sims [1998a], I develop an argument that we should expect all reactions of individuals to

external signals to behave to a linear approximation like relations that involve both lags (apparentinertia) and idiosyncratic random errors.

6

Table 1

Identifying Restrictions

VariablesEquations IP CPI Currency M1 Discount Pcomm

IP x - - - 0 0CPI x x - - 0 0

Currency x x x - 0 0M1 x x x x 0 0

Policy 0 0 x x x xPcomm x x x x x x

The restricted A0 matrix is almost, but not quite, in triangular form. Furthermore, it has only 20,not 21 free coefficients, meaning that the A polynomial has one less coefficient than theunrestricted reduced form model. Iterative methods are therefore required to estimate the model,but they can be executed quickly and reliably.7

II. Postwar results

A. The patterns of response to policy and of policy

When this model, with the order of A (the number of lags) set to seven, is estimated over thefull 1948:8-1997:10 sample period, the result implies the pattern of responses to behavioraldisturbances displayed in Figure 1. Each small graph shows the pattern of response of thevariable that labels its row to the disturbance that labels its column. The center line is theestimated response itself, and the upper and lower lines define a 90% probability band for theresponses.8 The column labeled “policy” shows the response of the rest of the economy to atypical (one standard-deviation) disturbance in the policy equation. It displays a pattern ofresponses that is familiar from the previous literature. Interest rates rise and then slowly begindrifting back toward the mean. Currency and M1 both fall and remain low. Commodity pricesand CPI both decline, with the decline in CPI small and delayed, while that in Pcomm issubstantial and immediate. IP falls and returns very slowly toward trend. The error bands showthat there is substantial uncertainty about the magnitude of the responses to policy, and in the caseof the CPI response, even about the sign of it.

7 The estimation also uses stochastic prior information, rather than ad hoc setting to zero of

insignificant coefficients, to control the bad effects of estimating so many free coefficients at once.The methods are based on ideas in Sims and Zha [1998a], though here they can be implementedentirely with “dummy observations”, making the calculations simpler than those described in thatarticle.

8 The bands are computed as Bayesian posterior probability bands, using the approachdescribed in Sims and Zha [1998b], except that the Monte Carlo simulations used the adaptiveMetropolis-Hastings algorithm described in Sims [1998b]. The bands were constructed from a500-element subsample of 5000 iterations of the simulation algorithm, which had an effectivesample size of about 500.

7

Figure 1

Responses to Identified Shocks, 1948:8-1997:10

Looking across a single row in the figure, the relative sizes of the plotted responses show therelative importance of the sources of disturbance labeled in the columns in generating variation inthe variable labeled in the row. We see from the discount rate row that policy shocks produce thelargest impact on the interest rate, but that others, particularly the Pcomm shock, the IP shock,and the M1 shock, are cumulatively more important in generating interest rate variation. That is,though policy disturbances account for a substantial fraction of variation in interest rates,particularly in the short run, most variation in them is generated by systematic responses todisturbances originating outside the policy equations. Furthermore, the system implies a distinctlyactive response of policy to disturbances that imply inflationary pressure. The three non-policyshocks that imply interest rate increases also are the three that imply the largest increases inexpected future CPI inflation and in current and expected future Pcomm levels.9 In the case ofPcomm shocks, the rise in interest rates is sufficient to produce a decline in the money stock in theface of the inflationary pressure, and in the case of IP shocks the interest rate rise is sufficient tohold the money stock essentially constant in the face of a rise in output and prices. The M1 shockdoes not show such a strong restrictive response to inflationary pressure. Interest rates rise, butonly with a delay, and M1 rises substantially. This looks like what might be expected if monetarypolicy partially accommodated an expansionary disturbance originating elsewhere, e.g. in anincreased current or expected future fiscal deficit.

1. Stability of behavior over time within the postwar periodThe rhetoric of monetary policy debate has certainly changed over the 1948-97 period.

Attempts to model the behavior of monetary authorities over this period (including the attemptrepresented by this paper’s model) can find statistically significant changes in behavior. TheLucas critique has conditioned many macroeconomists to think in terms of “regime shifts” as theonly internally consistent way to think about improving policy, and hence to look for themstatistically.10 Why then does this paper present results from a fixed-coefficients linear model fitto the entire 1948-97 period?

There are several arguments in favor of sticking with a fixed model for the period.

• Tests for shifts in regime based on conventional significance levels are inconsistent, in thetechnical econometric sense. This is not a strong argument here, since we do not actuallybelieve in a literally fixed model. Nonetheless, the problem is symptomatic of a broaderproblem with conventional tests – in large samples, they will reject the hypothesis ofparameter constancy even in cases where the parameter changes detected are triviallysmall.

9 CPI shocks, which do not generate a strong interest rate response, account for a substantial

part of variation in the level of CPI but they move the level in a single step, without implyingmuch expected future inflation.

10 Macroeconomists who think this way are mistaken. See section V below.

8

• Shifts in policy rule of modest size, sustained over only a few quarters or years, may havebeen quite non-random from the point of view of some participants in the policy process atthe time, or from the point of view of ex post statistical analysis, while still having beenperceived as unpredictable randomness from the point of view of economic agents.

• As always in statistical modeling, we face a tradeoff of bias versus precision. The morecomplex a scheme of variation in policy behavior parameters we allow for, the less precisecan be our estimates of that scheme. We may be sure that a fixed model is not theabsolute truth, while believing that nonetheless its bias is small enough that we wouldobtain worse results with a model that allowed for shifts in policy behavior.

• Using statistical criteria that explicitly gauge the tradeoff of bias with precision and thatovercome the inconsistency problem in conventional statistical tests, we conclude thatmodels that allow no change in parameters are preferred.

The quantitative evidence is that, comparing the fit of a single model fit to 1948-97 with thatof two separate models, in which all parameters, including the residual covariance matrices, are fitto the separate periods 1948:8-1979:6 and 1979:7:1997:10, twice the difference in log likelihoods(a statistic we will here call S) is 849.3379. The difference in numbers of free parameters is 279.Conventional statistical tests, based on asymptotic theory and using a 5% significance level,would certainly reject the null hypothesis of no change in parameters. The Akaike criterion,which aims at improving forecast performance but does not overcome the inconsistency ofconventional tests, rejects for S exceeding twice the degrees of freedom, which would here be athreshold of 558. The most widely used consistent model selection criterion is the Schwarzcriterion, which compares S to degrees of freedom times log of sample size, here leads to athreshold of 1780, so that the fixed model is strongly favored. Another consistent criterion, whichfavors smaller models less strongly than Schwarz’s, is the Hannan-Quinn criterion. It compares Sto the degrees of freedom times twice log(log(sample size)) and here leads to a threshold of 1034,again strongly favoring the fixed model.11

That consistent model-selection criteria favor a fixed model is all the more remarkable giventhat the tests allow for changes in disturbance variance as well as changes in the coefficientsthemselves. Monetary policy from late 1979 through 1982 was announced as allowing forincreased variation in interest rates, and the variance of changes in interest rates, including thediscount rate, was indeed much higher in this period than in the rest of the postwar period. But

11 For more discussion of these criteria, see e.g. Lütkepohl [1991], section 4.3. In

constructing these statistics, the model was estimated in reduced from and the stochastic priorinformation used in constructing the estimated responses was not used. Because of the tendencyof models estimated without use of stochastic prior information to be biased toward stationarityand to imply excessively accurate long-run predictions from sample initial conditions, testing forsample breaks this way is problematic. However, use of prior information would probably reduce,not increase, evidence of differences across subsamples. If data on the commercial paper ratereplaces that on the discount rate, the twice-log-likelihood-difference statistic becomes 969,which still gives the same conclusion by both the Schwarz and Hannan-Quinn criteria, though it issomewhat less strongly in favor of the fixed model than are the results with the discount rate.

9

this in itself does not imply a change in the shape of any of the responses plotted in Figure 1. Infact, it could be accounted for simply by increasing the variance of the disturbance to themonetary policy equation (which would imply increasing the relative size of the policy column ofFigure 1 during this period, without changing its shape or that of other columns). If we allow fora change in the variance of the policy equation disturbance in this period, while otherwise holdingmodel parameters fixed, we will account for most of the evidence of parameter change in the datawithout requiring any alteration of our conclusions on the shapes of policy responses.12

It might be supposed that, since the 1979-82 period was so clearly unusual, it would be betterto simply omit those years in fitting the model and to make our checks for parameter stabilityomitting those years as well. But these years, precisely because they showed so much variabilityin interest rates, provide strong evidence on the effects of monetary policy. Omitting themsubstantially increases the uncertainty in estimates of the model. The best procedure would be toweight the observations in this period for the policy equation lower, in proportion to the highervariance of the period, while still using all the data, but we proceed with estimates that simply usethe full sample without weighting.13

III. Interwar results

Applying the same set of identifying restrictions to the interwar period 1919:7-1939:12, wefind the responses displayed in Figure 2. The column corresponding to the effects of policydisturbances is qualitatively very similar to that in Figure 1. Note, though, that the scale on theoutput, CPI, and currency rows is more than double the scale on the corresponding rows for thepostwar Figure 1. Because this period is shorter, the error bands are somewhat wider than forFigure 1.

Output shocks in the interwar period educed a much more accommodative response ofmonetary policy than did the smaller corresponding shocks in the postwar period. In the laterperiod, a typical-sized output shock of about 1.5% generated an increase of the discount ratewithin a year of about 13 basis points. This was enough to keep M1 from increasing at all, and tokeep the rise in commodity prices to about 1.3%. A corresponding shock in the interwar periodraised output by 3.8% within the year, yet produced a rise in the discount rate of less than 5 basispoints. This was reflected in M1’s expanding with output, by about 1%, and in greater inflation,measured both by commodity prices and especially by the CPI.14

An especially interesting difference between the periods shows up in the currency shockcolumn. Interwar currency shocks moved currency and M1 strongly in opposite directions, andthe discount rate followed currency, not M1. Periods when people converted bank deposits tocash, corresponding to periods with positive currency shocks, reflected worries about the

12 It would of course be a good idea to check this assertion directly, and it is hoped that a later

draft of this paper will do so.13 It is hoped that a later draft of this paper will carry out the suggested weighted estimation.14 Bear in mind that this is a linear model, so it makes no distinction between increases and

decreases. In the interwar period, monetary accommodation was of course often accommodationof recession and deflation, not of growth and inflation.

10

solvency and liquidity of the banking system. It is noteworthy that interwar monetary policyapparently accelerated the shrinkage in money by tightening – raising the discount rate – asdeposits were draining out of the banking system.

To disturbances other than currency shocks, responses of the discount rate were generallysmaller and more delayed in the interwar period, despite the large sizes of the shocks as measuredby their effects on other variables.

Figure 2

Responses to Identified Shocks, 1919:8-1939:12

IV. The contribution of monetary policy to fluctuations

We can see directly from Figure 1 and Figure 2 that the proportion of variability in IP in eitherperiod that is accounted for by disturbances in monetary policy is estimated as small. This followsfrom the fact that in the first row of the figure, all responses are much smaller in magnitude thanthe responses to IP shocks themselves. We can summarize what can be seen from the figures byallocating to the sources of disturbance the variance of forecast errors in all variables over thefour years displayed in the figure. These allocations are summarized in Table 2 and Table 3.Each row of these tables sums to 100%, and shows where variation in the variable labeling therow originated during the period. Industrial production is accounted for mainly by its owndisturbances in both periods. The discount rate is accounted for more by responses to variablesother than policy than by policy disturbances in the postwar data, but the reverse is true in theinterwar data.

Table 2

48-Month Horizon Variance Decomposition, 1948-79IP CPI Currency M1 P olicy Pcomm

IP 79% 1% 1% 5% 6% 8%CPI 20% 21% 4% 19% 1% 35%

Currency 19% 1% 53% 14% 13% 1%M1 1% 0% 5% 83% 3% 8%

Discount 26% 0% 3% 11% 22% 37%Pcomm 13% 1% 1% 17% 19% 50%

Table 3

48-Month Horizon Variance Decomposition, 1919-39IP CPI Currency M1 P olicy Pcomm

IP 83% 1% 4% 3% 3% 7%CPI 30% 41% 0% 1% 10% 17%

Currency 3% 0% 44% 7% 43% 2%M1 29% 1% 23% 26% 11% 9%

Discount 1% 9% 20% 2% 53% 15%Pcomm 30% 4% 1% 1% 8% 57%

11

Results like this do not of course directly imply that monetary policy is unimportant to cyclicalfluctuations. They imply only that unpredictable variation in monetary policy as beenunimportant. It could be true that monetary policy has been highly systematic and predictable, yetalso that it could have greatly changed the pattern of fluctuations if it had taken a different course.We can use this model to gain some insight into how the economy’s behavior might have differedhad monetary policy been systematically different. Indeed, we have seen that there are notabledifferences in the way the discount rate responded to the state of the economy in the interwar andin the postwar periods. The differences are largely in the direction that most economists wouldagree improves monetary policy: in the postwar period interest rates rise more quickly and sharplyin response to disturbances that predict inflationary pressure, and there is less tendency for thediscount rate to rise when the public starts to substitute cash for deposits. At the same time,fluctuations have been smaller in the postwar period. Maybe the changes in the systematicbehavior of monetary policy have been responsible for some of the improvement.

The modeling framework used here allows us to answer this question directly. We do so byexcising the monetary policy equation of the system, the fifth row of the set of dynamic equationsdisplayed in (1), from the model of one period, transplanting it into the model for the other periodas a replacement for the original policy equation of that model, and observing how the resultingchimera behaves.15

A. Replaying the great depression with postwar monetary policy

Consider first the outcome of sending an average of Arthur Burns, Paul Volcker, etc. back intime to manage the Federal Reserve System in the 20’s and 30’s. The impulse responses of thegrafted system are displayed in Figure 3, alongside the originally estimated responses for the1919-39 period.

Changing the policy equation has a noticeable, if not large, effect. CPI and M1 respond lessto IP shocks and to commodity price shocks with the postwar policy, while currency respondsmore. However the effect on IP’s responses to shocks is very small. IP shocks have a slightlyless persistent effect on IP with the postwar policy. Perhaps surprisingly, the postwar policybehavior raises interest rates following an interwar currency shock, just as did the actual interwarpolicy. The increase in discount rate following this shock is less persistent than it was in theactual interwar data, but this does little to dampen the outflow of deposits as currency increases.

15 In doing this, we are “subject to the Lucas critique”. The reflex reaction of many

economists that this makes such exercises internally contradictory or misleading is mistaken. Wetake up this point at more length below. In the meantime, the reader is urged to proceed to seehow interesting the results are before assessing whether they must be dismissed on doctrinalgrounds.

12

Figure 3

Responses: 1919-39 model actual and counterfactual

What would have been the historical outcome if these responses had characterized actualinterwar monetary policy? We can answer that question by feeding the actual historical initialconditions and shocks through our 1919-39 “chimerical VAR”. Because the variables in thesystem are in some cases indexes whose base years do not match across the two periods, theconstant term in the policy equation requires adjustment, and there is no unique best way tochoose the adjustment. The results we present choose the constant so that when current andlagged values of all variables are set at their means over the 1919:1-7 initial conditions period, thepolicy equation has a zero residual. This leads to simulations in which, as in Figure 4, thediscount rate becomes negative after 1930. By choosing the constant term somewhat higher, thecounterfactual discount rate can be kept positive. We present the results with the discount rategoing negative because with the higher constant term, and thus tighter monetary policy, thedifferences between actual and counterfactual IP paths are smaller. Since the differences areremarkably small even when the non-negativity bound is ignored, we show these results tounderline the model’s implications for the limitations of monetary policy in counteracting theforces that generated the great depression. Each of Figure 4 through Figure 9 shows three lines –actual data, simulated data using the postwar policy behavior function and no disturbances, andsimulated data using the postwar policy behavior function with the disturbances from the original1919-39 policy behavior function.

With postwar policy, the discount rate would have dropped sharply during the 1920-21recession, and the model implies that this would have somewhat accelerated the recovery ofproduction and sharply curtailed the associated decline in the price level and the money stock.The discount rate would have dropped more sharply during 1929-30 at the onset of thedepression, according to the simulation that includes policy disturbances, and by about the sameamount as the actual discount rate decline according to the simulation without policydisturbances. The simulations imply, adjusted for the fact that interest rates cannot in fact bemade negative, that discount rates would have been at approximately zero throughout 1930-39.Note, though, that the rise in rates in September 1931, associated with Britain’s departure fromthe gold standard, is partially reproduced in the results without policy shocks. The rise is not sogreat, and starts earlier, but is still there.

Figure 5 shows that the (infeasibly) greater ease of the simulated monetary policy is implied tohave increased the level of output at the end of 1939 by about 18% compared to the actualoutcome, adding about 1.2% per year to the mean growth rate over 1924-39. However, it shouldbe borne in mind that the statistical accuracy of the model deteriorates at long horizons. Thus thiseffect on the long term growth rate is very uncertain, with a zero effect quite possibly within areasonable error band. When we consider the effects of the postwar policy on the cyclicalmovements within the period, we see very modest changes in the path of IP. The drop in IP from1929-33 is completely unaffected by the altered monetary policy. Recovery from 1933-37, therenewed recession thereafter, and the recovery again through 1939, all reappear in roughly thesame form and magnitude despite the altered monetary policy.

13

Figure 4

Figure 5

The postwar policy would have cut short the 1920-21 deflation, and it would have moderatedthe decline in CPI during 1929-33, as can be seen from Figure 6. In the 1929-33 period CPIdecline would have been about 20-25%, instead of 30%. Figure 9 shows that the 1920-21 declinein commodity prices would, like that in CPI, have been cut short by postwar monetary policy.But after that period, the postwar monetary policy makes little difference to the time path ofinterwar commodity prices. Currency and money supply growth would have been substantiallygreater, as can be seen from Figure 7 and Figure 8, but the cyclical pattern of the movements inthese two simulated series remains close to that of the series’ actual paths.

Figure 6

Figure 7

Figure 8

Figure 9

The results taken together imply that postwar policy reactions would have reproduced muchof the cyclical pattern in interest rates and money stock that actually occurred. Postwar policyreactions might well have led to a less restrictive monetary policy on average over the period (asin our simulations), but greater policy ease would have had only modest effects on the path ofprices and even more modest effects on the path of output, despite substantial effects on the longterm growth rate of money and currency.

These results, it must be remembered, treat all disturbances that arise from crises ofconfidence in the banking system or speculative pressure on gold reserves as non-policydisturbances. Bernanke [1983] has pointed out that bankruptcy and bank failure seem to haveplayed a role in the propagation of the great depression beyond what can be accounted for bytheir effects on the money stock. The calculations here suggest that movements in interest ratesand the quantity of money in themselves may have been rather unimportant, but they leaveBernanke’s arguments in full force. In fact, it might well be argued that if monetary policy hadsucceeded in expanding currency and deposits as rapidly as is assumed in this paper’scounterfactual simulation of the interwar period, at least some of the bank failures of the 30’smight have been avoided. Large scale bankruptcies and bank failures do not occur in ordinary

14

times, so to a linear model they appear as external disturbances, but they might in fact have beendampened by a persistent commitment to monetary ease.

But would a policy of ease of the sort simulated here have been feasible? And would it havebeen monetary policy? The simulations show that to inflate the growth of money would haverequired pushing the discount rate down to about zero. Furthermore, it would have requiredconvincing banks to expand. When interest rates on the securities it buys in open marketoperations have reached zero, a central bank’s open market operations cease having any effect onthe private sector’s overall portfolio: they simply replace one non-interest-bearing governmentliability with another. Banks were holding large amounts of reserves at this time. It seemsunlikely that they would have made much of a distinction between holding non-interest-bearingdeposits with the Federal Reserve system and holding non-interest-bearing government securities.

To affect bank behavior, the Federal Reserve would have had to open the discount window,and to do so systematically. That is, it would have had to offer to discount bank loans at anattractive rate and to do so in a way that would attract banks to the discount window on a largescale. It is true today that discounting of bank assets by government agencies, when carried outon a case by case basis and subject to a determination of “need”, cannot attract large scale use bybanks because it becomes a signal of financial distress. This was true also, and probably to aneven greater extent because of the widespread concern about bank solvency, during the greatdepression.16 We have seen that in fact there was a tendency to increase the discount rate in theface of disturbances that tended to increase currency and shrink deposits. This behavior, I wouldargue, is not a simple mistake, but arises naturally when the central bank is reluctant to or legallyforbidden to take on essentially fiscal commitments. Open market operations in short termgovernment securities denominated in dollars have no appreciable effects on the riskcharacteristics of the central bank’s portfolio. Acquisition of rediscounted private sector loans ata time when the economy is declining and there is widespread concern about bankruptcy is in thisrespect quite different, and was certainly understood to be different at the time of the greatdepression. At least potentially, it presents a substantial risk of losses. To undertake such riskwithout undermining confidence in the central bank itself, the central bank must have fiscalbacking. That is, it must be understood that, were there to be substantial losses on the privateassets being acquired, the central bank would be kept solvent by government budgetary action.17

That in a deflationary crisis the line between monetary and fiscal policy blurs is not anaccident, but a reflection of a general principle. Starting with Leeper [1991], the FTPL literaturehas brought out the interdependence of monetary and fiscal policy regimes in guaranteeing a

16 See Friedman and Schwartz [1963], p.325, e.g.17 The recent international monetary crises have brought this point sharply into relief in some

cases. For example, in the 1994 peso collapse in Mexico, the central bank discounted a largequantity of bank debt that proved to be bad. In 1998, there is a political struggle over the fiscalmeasures needed to cover this transaction, and the delay in resolving it is causing continueddifficulties for the banking system. This seems to have been an instance where the central bankacted on the assumption that it had fiscal backing, the fiscal backing has since come into doubt,and the result is that the original effect of increasing confidence in the banking system is beingpartially unraveled. (See Business Week, June 22, 1998, p.62.)

15

unique price level. One combination of regimes, labeled “active money, passive fiscal” by Leeperand “active money, Ricardian fiscal” by Woodford, involves a commitment by the monetaryauthority to raise nominal interest rates by enough to raise real interest rates when inflation rises,accompanied by a commitment by the fiscal authority to increase primary surpluses via taxation orexpenditure reduction by more than enough to cover the increased interest expense implied by therise in nominal rates. In such a pairing of regimes, the price level is determined by monetarypolicy, in the sense that stochastic shocks to the monetary policy rule impact directly on prices,while stochastic shocks to the fiscal rule have no effect on prices. It seems that this kind ofpairing of regimes characterizes most advanced economies most of the time.

However, as Ben-Habib, Schmidt-Grohe, and Uribe [1998] have recently emphasized, thispairing of regimes does not deliver global uniqueness of the price level. The commitment bymonetary authorities to raise rates when inflation advances must be matched by a correspondingcommitment to lower them when inflation recedes, and to lower them further when inflation isreplaced by deflation. So long as one component of the government debt is non-interest-bearingcurrency, it will not be possible to make nominal interest rates negative. But this means that ifevents force the monetary authority, following its “active” rule, into near-zero-interest-rateterritory, it must eventually lose its ability to move rates in the same direction as inflation and byenough to lower real rates as inflation declines. The passive or Ricardian fiscal policy thatcouples with an active monetary policy to deliver a determinate price level becomes a source ofindeterminacy in circumstances where the monetary authority has lost the ability to respondstrongly to changes in inflation with changes in interest rates. Determinacy of the price levelwhen monetary policy is forced to leave the nominal rate fixed requires a fiscal commitment tokeep the real primary surplus insensitive to changes in the real value of outstanding governmentdebt. If all interest rates, including long rates, fell to zero, this would mean no more than that thebudget surplus should not increase with deflation. But long rates are likely to remain positiveeven if short rates are driven near to zero.18 The required fiscal commitment then is that theconventional deficit should increase with deflation by more than enough to offset any rise in thereal value of interest expenditures due to deflation. Putting the matter more broadly, in adeflationary crisis the problem is that government liabilities in general are too attractive relative toprivate sources of wealth. Countering the deflation requires policy action that decreases theexpected return on government liabilities. Budget deficits, or reduced surpluses, if perceived as apermanent change in fiscal policy, can accomplish this. Open market operations in governmentsecurities cannot.

A related exercise was undertaken by McCallum [1990]. He concludes that a monetary baserule could have largely eliminated the great depression. The difference in results comes fromseveral sources. He deliberately refrains from modeling prices and real output separately,concentrating entirely on whether nominal GNP could have been kept stable. The modelestimated in this paper implies stronger influence of monetary policy on prices than on output forthe interwar period. McCallum also uses a model with simple dynamics and strong a priorirestrictions. Most importantly, his model includes no recognition of the fact that monetary policy

18 Yields on 12-year government bonds averaged 3.6% in 1929 and did not fall below 2%

from then through 1939 (See Board of Governors of the Federal Reserve System [1943], Table130.

16

reacts to the state of the economy, and that this should affect the interpretation of estimatedregression equations.

B. Replaying postwar history with interwar monetary policy

The interwar period involved such large cyclical disturbances that the relatively modest effectof changing the monetary policy rule on the implied outcomes for that period may not berepresentative of the effect of changing policy rules in more stable periods. It is thereforeinteresting to reverse the experiment of the previous section, replacing postwar monetary policywith interwar policy in the postwar model.

Figure 10 shows the effect of the change on responses to disturbance. The change in the waythe discount rate responds to non-policy disturbance is substantial. IP, M1, and Pcommdisturbances, all of which imply future inflation, produce interest rate responses of the same signwith the interwar as with the postwar reaction function, and after several years the responsesachieve similar magnitudes, but the postwar responses are much quicker. This difference hasnoticeable effects on the responses of commodity prices to the same shocks, with commodityprices responding less under the postwar policy. However IP and CPI respond in much the sameway with either policy rule. There is an effect, with CPI inflation and IP responses less under thepostwar policy, but the effect is quite small.

Figure 10

Responses to identified shocks, postwar, actual and counterfactual

If we rerun postwar history with the interwar reaction function, we find in Figure 11, as wouldbe expected from the impulse responses, notable differences in the history of the discount rate.The counterfactual discount rate is lower in the 60’s and the first part of the 70’s than the actualrate, then rises faster than the actual discount rate. The simulation without policy shocks has therate rising earlier in the 70’s than the actual path, but then not rising quite as high in the early80’s. When policy shocks are added, the rise of rates from the late 70’s to the early 80’s isreproduced almost exactly, in timing and magnitude. The interwar policy rule keeps rates highnotably longer than did the actual path of policy.

In Figure 16 we see that the earlier rise of rates in the 70’s in the no-policy-shock simulationproduces a sharper temporary reversal of commodity price inflation, so that by the early 80’scommodity prices are on almost the same track in the no-policy-shock as in the policy-shockcounterfactual path, despite the less pronounced peak in rates under the former path.

Figure 12 and Figure 13 show, perhaps surprisingly given the small differences in responses toshocks in Figure 10, that the difference in policy has noticeable effects on the time paths of CPIinflation and IP. The low interest rates through the early 70’s under the interwar policy producegreater CPI inflation, and this is accompanied by higher output growth. The higher inflationeventually requires interest rates just as high under the interwar as under the postwar policy,however, and as these bring inflation down, they also slow output growth. The recession of theearly 80’s is larger under the interwar policy, and the growth rate of IP remains generally lowerunder the interwar policy until the early 90’s.

17

There is some plausibility to this analysis of how outcomes might have differed with amonetary policy that, like the interwar policy, responded less promptly to inflationary anddeflationary pressure, but the statistical caveats mentioned earlier bear repeating here. The effectson CPI and IP are visible on a time scale of 5 or 10 years for the most part. This is why they aremore visible on the plots of simulated history than they are on the impulse response graphs, whichcover only four years. But responses at longer time horizons are less reliably estimated, so thedifferences found, while interesting, may be statistically unreliable.

At business cycle frequencies, IP fluctuations are very similar for all three lines plotted inFigure 12. It seems likely that the NBER business cycle chronologies would have looked quitesimilar with any of these paths. Putting the matter another way, the size and timing of thepostwar US recessions had little to do with either shocks to monetary policy or its systematiccomponent.

It also seems clear from the simulations postwar monetary policy is not as much different frominterwar policy as might have been imagined. Estimates of policy responses to inflationary andbanking system pressures obtained from data on the 20’s and 30’s reproduce the qualitativefeatures of postwar monetary policy responses. They also trace the history of interest rate risesduring the accelerating inflation of the 70’s much as they occurred in fact.

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

V. What about the Lucas critique?19

The analytical framework of this paper is one in which all policy actions, hypothetical orhistorical, are regarded as realizations of random variables. The task of econometric model

19 The first part of this section reviews long-standing philosophical disputes on which I have

stated my views many times before. It is only because my views on these issues seem still to becontroversial in some quarters, and perhaps incompletely understood, that I review them here.

18

identification is that of constructing a model that contains a component describing how theconditional distribution of economic outcomes varies as the random variables characterizingpolicy take on different possible values. Our modeling approach does this, and it is thereforelegitimate to use it to discuss counterfactual history or to project the future of the economy undervarious policy choices as a guide to policy formulation. There is no other approach to policyevaluation that recognizes the existence of uncertainty and that is internally consistent.

The Lucas critique of econometric policy evaluation can be formulated in a variety of ways.At its most straightforward, it points out that in a stochastic model that explicitly models thedynamics of expectations formation, evaluating changes in policy rule as if they could be madepermanently, while leaving expectations formation dynamics unchanged, is a mistake. Thisversion of the critique clearly does not apply to this paper’s analysis, as the models being usedcontain no explicit expectations-formation dynamics. Another version of the critique makes it awarning about the potential importance of a particular type of nonlinearity. Every appliedeconomist understands that the linear (or otherwise mathematically simple) models we use areapproximations valid over a certain range. The conventional version of this point is that it isdangerous to extrapolate results from a linear regression to independent variable values muchlarger or smaller than those actually observed in the sample. Lucas’s analysis made clear that indynamic macroeconomic models the absolute size of changes in random variables beingconditioned on in making projections is not the only worry. Sequences of values for conditioningrandom variables that are historically unprecedented in their serial correlation properties – likepersistently high or low money growth rates or interest rates – might make models run astray evenwhen they are not outside the range of historical experience in absolute size. This version of thecritique does apply to this paper’s analysis, and we need to consider it.

A third version of the critique makes it into a philosophical puzzle akin to Zeno’s paradox.Policy properly understood, from this viewpoint, is the policy rule. Since without changing therule we will not change the stochastic process describing the economy, no intervention that leavesthe rule intact produces any real change. Hence discussion of policy by economists should belimited to discussion of changes in policy rule. As a corollary, changes in policy will always haveto be accompanied by an analysis of how the change in rule affects private behavior viaexpectations formation. But once we recognize that the parameters of the rule can change, andthat a rational public is aware that they can change, then we must also recognize that theparticular values of the parameters of the rule that are chosen are realizations of random variables,for which the public, assuming rational behavior, knows the true probability distribution. We arethen back at square one; changes in the parameters of the rule itself are mere realizations ofrandom variables, generating no real change in the probability distribution of the economy.20

The fallacy in this third version is its assumption that change in policy that does not change theprobability distribution of economic outcomes is trivial. Two economies whose probability

20 A clear exposition of this viewpoint, bringing out its nihilistic implications for the possibility

of internally consistent policy evaluation, is in [Sargent 1984]. That paper also contains anarticulation of another position, even more nihilistic (that policy makers are always behavingoptimally), that Sargent incorrectly (but apologetically) attributes to me. My own views on thisare articulated at more length in Sims [1987].

19

distributions are the same may have very different actual realized histories. If the probabilitymodel is non-stationary or nearly so, as are most economic models, they may even have differenthistories when averaged over time.

Our attention then focuses on version 2 above. Are we conditioning on variations in policy sogreat that it is implausible that the public would view them as realizations of a fixed probabilitylaw for policy behavior? If we had found drastically different behavior of the economy as weswitched policy rules, this would be a strong caveat to the results. But we found differences thatwere for the most part quite modest. Of course if actual policy followed either of the no-policy-shock rules, the public would quickly discover the perfectly fitting regression equation thatdetermines policy reactions and build it in to their expectations. This would lead to much morecertainty about monetary policy than there is in fact. In this sense our simulation of these rules isunrealistic, as it ignores the reduction of uncertainty about monetary policy that they would entail.But clearly we are thinking of these simulations as representative of similar rules which stillcontain error terms. We display them only to give some insight into how much of historical policybehavior is attributed to the historical pattern of realized random policy disturbances.

Also, we have already made the point that there is probably an important nonlinearity lurkingin the interwar results that could be seen as a version of the Lucas critique idea: A policy thatsucceeded in expanding bank deposits as rapidly as our counterfactual interwar policy wouldprobably have had to entail increasing confidence in bank liquidity and solvency. It might welltherefore have eliminated or reduced some of the financial crisis shocks that the model treats asunrelated to monetary policy.

But on the whole, it appears that these considerations are only one of many reasons to besomewhat cautious about these results, not a reason for ignoring them. The postwar simulationsdo involve persistent differences from historical patterns in rates of monetary expansion and priceinflation. If the historical pattern had shown extremely stable inflation around a fixed mean, thiswould be strong reason for concern. Historical dynamics might then have reflected a public thathas a strong tendency to forecast rapid mean-reversion in inflation. But historical postwar USexperience shows a complicated pattern of near-non-stationary drift in inflation rates. Actualrational expectation-formation therefore must have involved recognition that the inflation rate candrift, and our simulated counterfactual patterns of drift are not far outside the range of actualexperience.

The identifying assumptions we have used in deriving our model are certainly legitimatelysubject to dispute, and altering those assumptions might alter results. These are much strongerreasons for questioning the results than the Lucas critique, which is after all just one particular lineof attack on a model’s identifying assumptions. In this case, it seems that there are otheridentifying assumptions that would be a better place to start.

VI. Conclusion

The assigned topic of this paper is the role of government as a source of business cycles. Webegan by limiting attention to the role of budgetary and monetary policy in generating businesscycles. We have developed a way of looking at historical data that allows us to consider bothwhether erratic variation in monetary policy has been an important source of fluctuations andwhether systematic patterns of response of monetary policy to the private sector has been

20

important in shaping business cycle fluctuations. The conclusion of our analysis is that evenduring the great depression, the role of interest rate policy in generating or propagating cycleswas modest. The systematic component of monetary policy has been remarkably stable, not onlywithin the postwar period, but between the interwar and postwar periods. Changes in thesystematic component of monetary policy of the magnitude seen between these two periodswould not have greatly changed historical business cycle chronologies, though it would probablyhave changed the postwar history of inflation. And random fluctuations in monetary policy alsodo not have effects large enough to substantially alter the economy’s business cycle chronology.

Analysis of the limitations of monetary policy during the 30’s, as interest rates approached azero lower bound, and consideration of the importance of disturbances related to financial crises,suggests routes by which government actions outside the bounds of normal interest rate policycould have had substantial effects, not modeled in this approach.

The overall conclusion might be that the aim of good monetary policy should be to makemonetary policy unimportant to the business cycle, and that postwar US monetary policy haslargely succeeded in this respect.

References

Ben-Habib, Jess, Stephanie Schmidt-Grohe [1998]. and Martin Uribe, “Monetary Policy andMultiple Equilibria”, NYU discussion paper available athttp://www.econ.nyu.edu/user/benhabib/research.htm.

Bernanke, Ben and Alan Blinder [1992]. “The Federal Funds Rate and the Channels of MonetaryTransmission,” American Economic Review 82, 901-921.

Cochrane, John H. [1988]. “A Cashless View of US Inflation”, presented in March at the NBERMacroeconomics Annual conference.

Bernanke, B. [1983]. “Nonmonetary Effects of the Financial Crisis in the Propagation of theGreat Depression”, American Economic Review, 73, 257-276.

Board of Governors of the Federal Reserve System [1943. Banking and Monetary Statistics,1914-1941.

Friedman, Milton [1958]. “The Supply of Money and Changes in Prices and Output,” in TheRelationship of Prices to Economic Stability and Growth”, 85th Congress, 2nd Session, JointEconomic Committee Print, Washington DC: US Government Printing Office. Reprinted inFriedman [1969], 171-187.

Friedman, Milton [1969]. The Optimum Quantity of Money and Other Essays. Chicago: AldinePublishing Company.

Friedman, Milton and Anna Schwartz [1963], A Monetary History of the United States 1867-1960, Princeton: Princeton University Press.

Garcia-Mila, Teresa [1987]. Government Purchases and Real Output: Empirical Evidence andan Equilibrium Model with Government Capital, University of Minnesota Ph.D. Thesis (titleof this reference may not be quite correct).

21

Baxter, M. and R.G. King, "Fiscal policy in general equilibrium," American Economic Review 83(June 1993), 315-334.

Leeper, Eric M. [1991], “Equilibria Under ‘Active’ and ‘Passive’ Monetary And Fiscal Policies,”Journal of Monetary Economics 27, February, 129-47.

Leeper, Eric M., C.A. Sims and Tao Zha, “What Does Monetary Policy Do?” Brookings Paperson Economic Activity, 1996:2.

Lütkepohl, Helmut [1991]. Introduction to Multivariate Time Series Analysis, Berlin,Heidelberg, New York, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest: Springer-Verlag.

McCallum [1990]McCallum, Bennett T. [1990]. “Could a Monetary Base Rule Have Preventedthe Great Depression?” Journal of Monetary Economics, 26(1), August, pages 3-26..

Sargent, Thomas J. [1984], “Autoregressions, Expectations, and Advice,” American EconomicReview Papers and Proceedings 74, May, 408-15.

Sims, C.A. [1987]. “A Rational Expectations Framework For Short Run Policy Analysis”, pp.293-310 in New Approaches to Monetary Economics, W. Barnett and K. Singleton, eds.,Cambridge University Press, 1987. Also available at http://www.econ.yale.edu/~sims.

Sims, C.A. [1994]. “A Simple Model for Study of the Determination of the Price Level and theInteraction of Monetary and Fiscal Policy,” Economic Theory 4, 381-399.

Sims, C.A. [1997]. “Fiscal Foundations of Price Stability in Open Economies”, presented at theJuly 1997 Far Eastern meetings of the Econometric Society. Available athttp://www.econ.yale.edu/~sims

Sims, C.A. [1998a]. “Stickiness”, processed, Department of Economics, Yale University.

Sims [1998b]Sims, C.A. [1998b]. “Adaptive Metropolis-Hastings Sampling”, processed, YaleUniversity.

Sims, C.A. and Tao Zha [1998a]. “Bayesian Methods for Dynamic Multivariate Models”,International Economic Review.

Sims and Zha [1998b]Sims, C.A. and Tao Zha [1998b]. “Error Bands for Impulse Responses,”second revision, processed July 1998.

Woodford, M. [1994]. “Monetary Policy and Price Level Determinacy in a Cash-in-AdvanceEconomy,” Economic Theory 4.

Woodford, Michael [1995]. “Price Level Determinacy without Control of a MonetaryAggregate,” NBER Working Paper No. 5204.

22

Data Appendix

I. Interwar

Except for IP, the series are from the NBER macro history database, which is accessible at

www.nber.org/databases/macrohistory/data/04/.

• IP: Federal Reserve code B50001

Industrial Production, total index, seasonally adjusted, from the Federal Reserve Board.

Accessible at http://www.bog.frb.fed.us/releases/G17/iphist/ip1ahist.sa

• CPI: NBER series: 04128Consumer Price Index, All Items, Bureau of Labor StatisticsUnits: 1957-1959=100Seasonal adjustment: NoneSource: BLS Release, Consumer Price Index--U.S.: All Items, 1913- 1960, Series A;Notes: Prior to 1953, this series was called the"index of cost of living." Data have beenconverted to the average 1957-1959 base by BLS. Prior to September, 1940, only fuel andfood components were monthly, all other components were priced at intervals of 3, 4, and6 months (see Survey of Current Business, May, 1941; also Monthly Labor Review,August, 1940, and BLS Bulletin nos. 699 (1941) and 966 (1949) for detailed information).The early segment of this series represents monthly interpolations by the Department ofCommerce.

• Currency: NBER series: 14125 Currency Held By The Public, Seasonally Adjusted Units: millions of dollars Seasonal adjustment: seasonally adjusted by source Source: Friedman And Schwartz, Monetary Statistics Of The United States (NBER,

1970), Table 27, Column 3, Pp. 402-415. Notes: Data represent vault cash of all banks subtracted from currency in circulation

outside the treasury and Federal Reserve banks. Data are for the Wednesday nearest theend of the month.

• M1: NBER series 14144 Money Stock, Commercial Banks Plus Currency Held By Public, Seasonally Adjusted Units: billions of dollars Seasonal Adjustment: Seasonally adjusted by NBER Source: Data are computed by NBER from the sum of series 14125 (currency held by the

public) and series 14145 (demand deposits adjusted and time deposits all commericialbanks); see Friedman And Schwartz, Monetary Statistics of The United States (NBER,1970).

Notes: Data are for the Wednesday nearest the end of the month.• Discount Rate: NBER Series: 13009 Discount Rates, Federal Reserve Bank Of New York Units: Percent

23

Seasonal Adjustment: None Source: Federal Reserve Board, Data For 1914-1922: "Discount Rates Of Federal

Reserve Banks, 1914-1921", 1922. Data For 1922-1969: Annual Reports For 1931-1942; Federal Reserve Bulletin, successive issues.

Notes: Data are computed by NBER by taking simple averages of rates for commercial,agricultural, and livestock paper, and weighting them by the number of days each rate wasin force. Data are for all classes and maturities of discount.

• Commodity Prices: NBER series: 04202 Units: 1947-1949=100 Seasonal adjustment: none Source: Ruth P. Mack,"Inflation and Quasi-Elective Changes in Costs," Review Of

Economics And Statistics, August, 1959 Notes: Series discontinued after January, 1957.

II. Postwar

All series except M1 (in part) were drawn from Citibase.

• IP: Citibase series name IP.

Industrial Production: total index (1992=100, SA)

• CPI: Citibase series name PUNEW

CPI-U: all items (82-84=100, SA)

• Currency: Citibase series name FMSCU.

Money Stock: currency held by the public, (bil$,SA)

• M1: Citibase series name FM1, spliced together with the NBER historical M1 series citedabove. The Citibase M1 series starts in 1959:1. The earlier data was scaled to match themodern series in 1959:1. Citibase title: Money Stock: M1 (currency, travelers’ checks,demand deposits, other checkable deposits), (bil$,SA)

• Discount Rate: Citibase series name FYGD.

Discount Rate, Federal Reserve Bank of New York (% per annum)

• Commodity Prices: Citibase series name PSCCOM.

Spot Market Price Index: BLS & CRB: all commodities (1967=100, NSA)